#286 ⟨a, b | aaabaaba=1⟩

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Properties

Complete rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
  1. cb ⇒ bc
  2. b4c3 ⇒ 1
  3. ca ⇒ ac
  4. b2a ⇒ ab2
  5. d ⇒ b4c2
  6. a2 ⇒ b2c2 
# ab:aaabaaba=1 bc/ad aaaa=c,baab=d magic:0
cb=bc
bbbbccc=1
ca=ac
bba=abb
d=bbbbcc
aa=bbcc

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

3 total

Σ#PresentationMapping
8299⟨a, b | aabaaaab=1⟩φ(a) = a, φ(b) = b
8302⟨a, b | aabaabaa=1⟩φ(a) = a, φ(b) = b
8322⟨a, b | abaaaaba=1⟩φ(a) = a, φ(b) = b